Academic Interests

My main research interests are in the philosophies of logic and mathematics, metaphysics and the philosophy of language. I am particularly interested in questions concerning ontology, individuation, essence, reference (especially to abstract objects), necessity and knowledge of necessary truths. My approach to these questions is broadly Fregean in that I relate them to questions in philosophical logic and the philosophy of language.

Linnebo, Øystein (2018). On the Permissibility of Impredicative Comprehension, In Jessica Leech (ed.),
Being Necessary Themes of Ontology and Modality from the Work of Bob Hale.
Oxford University Press.
ISBN 9780198792161.
kapittel 9.
s 170
- 189

I present a novel interpretation of Frege's famous attempt at Grundgesetze I §§29-31 to prove that every expression of his language has a unique reference. I argue that Frege's proof is based on a contextual account of reference, similar to but more sophisticated than that enshrined in his famous Context Principle. Although Frege's proof is incorrect, I argue that the account of reference on which it is based is of potential philosophical value, and I analyze the class of cases to which it may successfully be applied.

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume's Principle. According to Frege's Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA--one having to do with Hume's Principle, the other, with the underlying second-order logic--and investigates how much of Frege's Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that this axiom cannot be proved in the theories that are predicative in either dimension.

I first argue that Frege started out with a conception of logic closer to Kant's than is generally recognized. Then I analyze Frege's reasons for gradually rejecting this view. Although I concede that the demands imposed by Frege's logicism played some role, I argue that his increasingly vehement anti-psychologism provides a deeper and more interesting reason for rejecting his earlier view.

Ordinary English contains two sorts of object quantifiers. In addition to the usual singular quantifiers, as in 'There is an apple on the table', there are plural quantifiers, as in 'There are some apples on the table'. This article provides a survey of recent discussions of the logic, semantics, and metaphysics of plural quantification, as well as of its various philosophical applications.